Ariel,
I wrote this to help students with time management:
https://airlinepilot.life/t/what-does-an-atp-student-need-to-do-to-be-successful/10421
Your primary instructor is the one to provide you with the endorsement for the check ride. So, it will be up to your instructor to decide if they will allow you to fly with another instructor. It’s a great idea. I did this when I was an instructor.
Tory